Confirmed cases that don't require hospitalization still must quarantine. I have to imagine regular check-ins with their doctor are a must up until they are tested again and confirmed negative.
The curve for active cases in New York has essentially flattened, but they're still getting over 500 new cases every day and this virus hangs around for weeks. The total has dipped a few times, but after the outbreak they had there you probably won't see a real dive in active cases for a while. It's part of what makes COVID-19 so deadly. It fucking overstays its welcome.